Magma-fracturing during melt migration is associated with the propagation of a pore-generating damage front ahead of high-pressure fluid injection, which facilitates the transport of melt in the asthenosphere and initiates dike propagation in the lithosphere. We examine the propagation of porous flow in a damageable matrix by applying the two-phase theory for compaction and damage proposed by Bercovici et al. (2001a) and Bercovici and Ricard (2003) in 2-D. Damage (void generation and microcracking) is treated by considering the generation of interfacial surface energy by deformational work. We examine the stability of 1-D solitary waves to 2-D perturbations, and study the formation of finite-amplitude, two-dimensional solitary waves with and without solenoidal (rotational) flow of the matrix. We show that the wavelength and growth rate of the most unstable perturbations are dependent on both background porosity and the presence of solenoidal flow field. The effect of damage on finite amplitude 2-D solitary waves is then examined with numerical experiments. Stably propagating circular waves become flattened (elongated perpendicular to gravity) for small porosity, or elongated (parallel to gravity) for large porosity with increased damage. We show that the weakening of the matrix due to damage leads to these changes in wave geometry, which indicates a transition from magmatic porous flow to dike-like or sill-like magma-fracturing as magma passes through a semi-brittle/semi-ductile zone in the lithosphere.